Three rods A,B,C of same length and same cross-sectional area are joined. Their thermal conductivity are in ratio 1:2:(1.5).If the ends of A and C are at 200degreescentgrade and 18degreescentgrade respectively, compute the temperature at the of A and B in equilibrium.

Suppose the thermal conductivities of the rods are 1x, 2x and 1.5x.

Length of the rods = L, Area = A

If the rods are connected in series the heat flow through them will be same.

Let ΔH1, ΔH2 and ΔH3 be heat flow in the three rods respectively in time Δt

ΔH1/Δt = ΔH2/Δt = ΔH3/Δt

ΔH1/Δt = ΔH2/Δt

=> ΔH1 = ΔH2

=> xA(T1 – 200)/L = 2xA(T2 – T1)/L-----(i)

ΔH2/Δt = ΔH3/Δt

=> 2xA(T2 – T1)/L = 1.5xA(18 – T2)/L---(ii)

Solving eq.(i) and eq (ii)

You can the values of T1 and T2

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